# Wilson's Theorem in Disguise

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The *American Mathematical Monthly* problem 10578 considers a sequence defined by recurrence equation with initial conditions and asks to show that is only an integer for prime .

Contributed by: Oleksandr Pavlyk and Brett Champion (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

It is easy to find a symbolic solution of the above recurrence equation:

The above fraction is an integer only for prime by virtue of Wilson's theorem.

## Permanent Citation